Convergence Of Extrapolated Method Of Non-Hermitian Linear Systems

There are many numerical methods to solve the matrix equations with the formAu = f, (A ∈ C^n×n, f ∈ Cⁿ)where u is the solution vector which is to be determined. Iterative methods are often applied if the matrix equation arises from discrete approximations to partial differential equations. These matrix equations are generally characterized by the property that the associated square matrices are sparse, i.e., a large percentage of the entries of these matrices are zeros. In this case iterative methods own many advantages over other methods. Furthermore, extrapolation methods are often applied to make sure the convergence of iterative methods or to accelerate the rate of convergence of iterative methods.In this paper, the extrapolated method for solving non-Hermitian linear systems is proposed and the convergence is analyzed. We give the optimum parameters and the optimum rate. Then we applicate the results to the saddle problem in which parameters can be easily computed.